USA AMC 12 2001 1 The sum of two numbers is S. Suppose 3 is added to each number and then each of the resulting numbers is doubled. What is the sum of the final two numbers? (A) 2S + 3 (B) 3S + 2 (C) 3S + 6 (D) 2S + 6 (E) 2S + 12 2 Let P (n) and S(n) denote the product and the sum, respectively, of the digits of the integer n. For example, P (23) = 6 and S(23) = 5. Suppose N is a two-digit number such that N = P (N) + S(N). What is the units digit of N? (A) 2 (B) 3 (C) 6 (D) 8 (E) 9 3 The state e tax where Kristin lives is levied at the rate of p% of the first $28000 of annual e plus (p + 2)% of any amount above $28000. Kristin noticed that the state e tax she paid amounted to (p + )% of her annual e. What was her annual e? (A) $28000 (B) $32000 (C) $35000 (D) $42000 (E) $56000 4 The mean of three numbers is 10 more than the least of the numbers and 15 less than the greatest. The median of the three numbers is 5. What is their sum? (A) 5 (B) 20 (C) 25 (D) 30 (E) 36 5 What is the product of all odd positive integers less than 10000? 10000! 10000! 9999! 10000! 5000! (A) (B) (C) (D) (E) (5000!)2 25000 25000 25000 · 5000! 25000 6 A telephone number has the form ABC−DEF−GHIJ, where each letter represents a different digit. The digits in each part of the numbers are in decreasing order; that is, A > B > C, D > E > F, and G > H > I > J. Furth
